Advanced Biostatistics Chapter 7: Gerig’s Phenolic Acid Synergy Study 17 April 2006

Fixed Chambers

data one;

do van=0,0.25,0.5; do c=1,2,3; fer=0;

input agr @@; c1=(c=1); c2=(c=2); c3=(c=3); output;

end; end;

do van=0,0.25; do c=1,2,3; fer=0.25;

input agr @@; c1=(c=1); c2=(c=2); c3=(c=3); output;

end; end;

do c=1,2,3; fer=0.5; van=0;

input agr @@; c1=(c=1); c2=(c=2); c3=(c=3); output;

end; datalines;

16.4720 11.3889 16.7488 9.2972 9.5356 10.1047 3.8527 3.5682 2.1378

1.8917 6.6595 6.4365 5.1907 7.7208 3.1990 0.8690 1.7302 0.9536

;

proc nlin data=one;

parms th11=16.5 th12=11.4 th13=16.7 th2=.2 th3=3 th4=1 th5=0;

z=fer+th4*van+th5*sqrt(th4*fer*van);

if z le .0001 then do;

th1=th11*c1+th12*c2+th13*c3;

model agr=th1;

end;

else do;

t=(z/th2)**th3; den=1+t; den2=den*den;

th1=th11*c1+th12*c2+th13*c3;

model agr=th1/den;

end; run;

Full Model

Sum of Mean Approx

Source DF Squares Square F Value Pr > F

Model 7 1142.6 163.2 43.38 <.0001

Error 11 41.3888 3.7626

Uncorrected Total 18 1184.0

Approx

Parameter Estimate Std Error Approximate 95% Confidence Limits

th11 15.2035 1.6566 11.5573 18.8496

th12 13.7524 1.6276 10.1700 17.3348

th13 15.9412 1.6722 12.2606 19.6217

th2 0.1936 0.0300 0.1275 0.2597

th3 2.7216 0.7358 1.1022 4.3410

th4 0.6259 0.1067 0.3911 0.8608

th5 -0.8266 0.1830 -1.2294 -0.4237

Reduced Model

Sum of Mean Approx

Source DF Squares Square F Value Pr > F

Model 6 1117.5 186.2 33.60 <.0001

Error 12 66.5230 5.5436

Uncorrected Total 18 1184.0

Approx

Parameter Estimate Std Error Approximate 95% Confidence Limits

th11 15.2556 2.0275 10.8380 19.6732

th12 13.6221 1.9906 9.2849 17.9593

th13 16.2120 2.0507 11.7438 20.6802

th2 0.1881 0.0480 0.0836 0.2925

th3 1.9243 0.6312 0.5489 3.2996

th4 0.5996 0.1593 0.2525 0.9466

Random Chambers

Full Model

proc nlmixed data=two;

parms th1p=14 th2=.2 th3=3 th4=1 th5=-1 sig=2 sigu=1;;

th1=th1p+u;

z=fer+th4*van+th5*sqrt(th4*fer*van); var=sig*sig; varu=sigu*sigu;

t=(z/th2)**th3; den=1+t;

mean=th1/den;

model agr~normal(mean,var);

random u~normal(0,varu) subject=c;

run;

Fit Statistics

-2 Log Likelihood 63.1

AIC (smaller is better) 77.1

AICC (smaller is better) 88.3

BIC (smaller is better) 83.3

Parameter Estimates

Standard

Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper

th1p 14.1681 1.9793 17 7.16 <.0001 0.05 9.9921 18.3441

th2 0.2101 0.02990 17 7.03 <.0001 0.05 0.1470 0.2732

th3 2.7474 0.4208 17 6.53 <.0001 0.05 1.8597 3.6352

th4 0.6683 0.06071 17 11.01 <.0001 0.05 0.5402 0.7963

th5 -0.8371 0.1337 17 -6.26 <.0001 0.05 -1.1193 -0.5550

sig 0.2319 0.3334 17 0.70 0.4962 0.05 -0.4716 0.9353

sigu 3.8165 0.9029 17 4.23 0.0006 0.05 1.9115 5.7215

Reduced Model

Fit Statistics

-2 Log Likelihood 76.0

AIC (smaller is better) 88.0

AICC (smaller is better) 95.6

BIC (smaller is better) 93.3

Parameter Estimates

Standard

Parameter Estimate Error DF t Value Pr > |t| Alpha Lower Upper

th1p 14.9694 1.2306 17 12.16 <.0001 0.05 12.3732 17.5657

th2 0.1896 0.03991 17 4.75 0.0002 0.05 0.1054 0.2738

th3 1.8796 0.5241 17 3.59 0.0023 0.05 0.7738 2.9853

th4 0.6006 0.1254 17 4.79 0.0002 0.05 0.3360 0.8653

sig 1.9400 0.3990 17 4.86 0.0001 0.05 1.0983 2.7818

sigu 0.9233 1.9548 17 0.47 0.6427 0.05 -3.2010 5.0475